oil interfacial tension at elevated temperatures and pressures: A molecular dynamics simulation study with biomolecular force fields

Accepted Manuscript Predictions of water/oil interfacial tension at elevated temperatures and pressures: A molecular dynamics simulation study with biomolecular force fields Konstantinos D. Papavasileiou, Othonas A. Moultos, Ioannis G. Economou PII:

S0378-3812(17)30182-6

DOI:

10.1016/j.fluid.2017.05.004

Reference:

FLUID 11475

To appear in:

Fluid Phase Equilibria

Received Date: 6 April 2017 Revised Date:

29 April 2017

Accepted Date: 4 May 2017

Please cite this article as: K.D. Papavasileiou, O.A. Moultos, I.G. Economou, Predictions of water/oil interfacial tension at elevated temperatures and pressures: A molecular dynamics simulation study with biomolecular force fields, Fluid Phase Equilibria (2017), doi: 10.1016/j.fluid.2017.05.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Predictions of water/oil interfacial tension at

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elevated temperatures and pressures: A molecular

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dynamics simulation study with biomolecular force

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fields

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Konstantinos D. Papavasileiou,1 Othonas A. Moultos,2 and Ioannis G. Economou1,3,*

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Nanotechnology, Molecular Thermodynamics and Modelling of Materials Laboratory,

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GR-15310 Aghia Paraskevi Attikis, Greece

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National Center for Scientific Research “Demokritos”, Institute of Nanoscience and

Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical,

Maritime and Materials Engineering, Delft University of Technology, Leeghwaterstraat

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39, 2628CB Delft, The Netherlands

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Texas A&M University at Qatar, Chemical Engineering Program, Education City, PO

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Box 23874, Doha, Qatar

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*To whom correspondence should be addressed

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IGE: [email protected] 1

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Abstract The interfacial properties of water/oil mixtures is a topic of significant interest for the oil and gas

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and chemical industry, as they are required for performing process calculations. However, the

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reported data at high temperatures and pressures are scarce. The present study focuses on

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simulating the interfacial tension (IFT) of mixtures of water with i) toluene (water/toluene), ii) n-

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dodecane

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(water/toluene/n-dodecane), at 1.83 MPa and temperatures ranging from 383.15 to 443.15 K.

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Molecular Dynamics (MD) simulations with atomistic molecular models, developed primarily

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for biomolecular systems were employed. In the simulations performed, the effects of the water

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model and the scaling of interatomic interactions by introducing a binary interaction parameter,

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kij , were assessed for the accurate reproduction of experimental data. The combination of the

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TIP4P/2005, SPC/E and TIP3P water models with the GAFF and LIPID14 force fields for

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toluene and n-dodecane respectively, coupled with appropriate binary interaction parameters, kij ,

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for the interaction of carbon with oxygen atoms were found to yield accurate results in the case

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of binary mixtures. For the water/toluene/n-dodecane mixture, all force field combinations tested

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resulted in overestimated IFT values for the whole range of state points examined. Our

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simulations show that these widely used force fields, originating from the world of biomolecular

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simulations, are suitable candidates in the study of binary water/oil mixtures. Nevertheless, the

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introduction of the kij scaling parameter is not sufficient to allow the accurate reproduction of

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experimental IFT data for ternary water/oil/oil mixtures.

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Keywords: Interfacial tension; toluene; n-dodecane; Molecular dynamics simulations

and

iii)

a

50:50

%

wt

toluene:n-dodecane

mixture

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(water/n-dodecane)

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1.

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The 9th Industrial Fluid Properties Simulation Collective Challenge [1] aimed at testing the

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ability of molecular modeling approaches to predict water/oil interfacial tension (IFT) at elevated

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temperatures and pressures for three different oils/water mixtures, namely water with toluene, n-

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dodecane and a 50:50 % wt mixture of n-dodecane and toluene. The IFT, γ, of water/oil systems

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is one of the basic physical properties required for performing process design calculations in oil

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and gas and chemical industry [2]. IFT is defined as the force per unit length that is required to

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increase the surface area between two immiscible fluids in contact [3]. It is an essential property

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for the description of liquid-liquid interfaces, as it controls contact phase hydrodynamics and

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mass transfer [4]. Experimentally, IFT is measured by a variety of methods, such as the spinning

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drop, the du Noüy ring, the Wilhelmy plate etc. [5, 6]. Previous IFT studies on binary water/n-

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alkane [7-9], water/toluene [8, 10, 11] and ternary mixtures of water/n-alkane/toluene [12]

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referred to ambient conditions. However, at high temperatures and pressures only a few data

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have been reported [4, 7, 13-18]. Typically, these conditions involve temperatures that reach and

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exceed 370 K, while pressures applied are normally beyond 0.1 MPa in order to maintain the

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liquid state. A common thread in these studies is the IFT tendency to decrease with increasing

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temperature at constant pressure. Pressure effects are shown to be less pronounced [7], with IFT

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increasing with increasing pressure at constant temperature [7, 19-21].

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Introduction

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Several simulation studies have been dedicated to the examination of the IFT water/oil

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mixtures. These include application of Monte Carlo (MC) [22, 23], Molecular Dynamics (MD)

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[24-28] and mesoscale modelling techniques such as Dissipative Particle Dynamics (DPD) [29]

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and Coarse-Grained Molecular Dynamics (CGMD) [30, 31]. CGMD methods have been

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enriched recently with force fields developed with the SAFT-γ Mie equation of state (eos) top3

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down approach, which has been successfully applied in MD simulations for the prediction of

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several water/oil mixture properties [32]. Within the framework of this challenge, we calculated

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the IFT of these mixtures by means of interfacial MD simulations, a robust and reliable

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simulation technique in the study of water/oil systems.

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The accuracy of the molecular models, describing the intra- and inter-molecular

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interactions, employed in simulations are of outmost importance for attaining accurate IFT

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values [33]. To this extend, our attempts focused on incorporating and benchmarking the

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performance of well-established atomistic molecular models coming from the world of

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biomolecular simulations in systems of interest to the chemical/petrochemical industry. More

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specifically, for the description of the organic phase we employed the General AMBER force

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field (GAFF) [34] and the Lipid14 [35] force field for toluene and n-dodecane, respectively.

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GAFF was developed for the incorporation of small organic molecules to existing AMBER force

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fields for proteins and nucleic acids. In early attempts of lipid simulations for a range of

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phospholipid bilayers GAFF showed great potential in the reproduction of experimental

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membrane properties, such as the area per lipid, the area compressibility modulus, lipid order

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parameters and others [36, 37]. However, reoccurring issues at long timescales and constant

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pressure such as a liquid-to-gel phase transition above the phase transition temperatures were

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observed [38-40]. Similar issues were observed also for the OPLS-AA force field for n-alkanes

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longer than n-hexane, thus prompting for the development of the L-OPLS force field [41], which

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was parameterized in order to accurate reproduce liquid densities and viscosities of long

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hydrocarbons [42]. Therefore, dedicated efforts to tackle these problems led to the development

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of a new family of lipid force fields based on GAFF, with Lipid14 being its latest variant.

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Lipid14 features optimized alkyl chain dihedral angle terms and Lennard-Jones (LJ) parameters,

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allowing for tensionless simulations of lipid systems. The key features of these models are their

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enhanced compatibility with and transferability to a wide range of physical systems, ranging

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from proteins, lipids to organic compounds [34, 35, 43].

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No prior attempts to utilize the Lipid14 in calculations of non-biological systems have

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been reported in literature. Recently, Kumar et al. [44] evaluated GAFF’s performance in the

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prediction of liquid−vapor saturation properties of naphthalene derivatives. GAFF exhibited high

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accuracy of the liquid−vapor saturation properties and thus was proved to be a reasonable choice

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for describing the phase behavior of systems relevant to the oil and gas industry. In addition, the

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computational benchmarking of 146 organic liquids by Caleman et al. [45] showed that GAFF

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performs well in the prediction of several properties such as density, enthalpy of vaporization,

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heat capacities, and others.

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We therefore grasped the opportunity of this 9th Challenge in order to evaluate the

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performance of these models in systems of industrial interest, which briefly encapsulates the

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novelty of the present work. In addition, we have examined the effect of the non-bonded LJ

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interactions long-range treatment, the simulation duration and the impact of the choice of the

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water model on the calculated IFTs.

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2. Simulation methods

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2.1. Force fields

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Toluene structure was initially optimized in the gas phase at the B3LYP/6-31G* level of theory

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[46-48], by means of the Gaussian 09 [49] suite of programs. Then, atomic charges were

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obtained from the optimized geometry at the HF/6-31G* level of theory according to the

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Mertz-Kollman population analysis scheme [50, 51]. Consecutively, partial atomic charges were 5

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derived according to the RESP protocol [52], utilizing the ANTECHAMBER module [53] of the

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AMBER12 suite of programs [54]. GAFF parameters [34] were then assigned to toluene, the

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atom types of which are presented in Table S1 of the Supporting Information. Topologies were

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generated by means of the tLEaP module [54] and are illustrated in Table S2, along with the

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calculated partial charges.

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n-dodecane was described by means of the Lipid14 force field parameters [35]. Partial

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charges for the n-dodecane chain were generated according to the original derivation procedure

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[35]. Specifically, fifty randomly selected n-dodecane molecules were extracted from the initial

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cubic box conformation and were subsequently used for the charge calculation. The Electrostatic

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Potential (ESP) [50, 51] was calculated directly from each structure at the HF/6-31G* level of

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theory without optimization, and partial charges derived using the RESP fitting procedure [52]

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for each chain. Charges were then taken as an average over all fifty RESP fits. The structure and

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partial charges of n-dodecane are illustrated in Table S3 of the Supporting Information.

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For the representation of water molecules the TIP4P/2005 [55], TIP3P [56] and SPC/E

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[57] models were employed. Our starting point was the TIP4P/2005 force field, which is a four-

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site rigid model with a LJ sphere fixed on the oxygen atom. The electrostatic contributions are

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implemented by positive partial charges assigned to the hydrogens and a negative partial charge

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on the additional site, located on the bisector of the H-O-H angle at a distance 0.1546 Å from the

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oxygen atom. The TIP4P/2005 model has been extensively tested and found to be very accurate

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for several water properties, including the vapor-liquid IFT [58-60]. On the other hand, the

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SPC/E and TIP3P force fields assume a single LJ site on the oxygen atom and three charges on

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oxygen and hydrogen atoms, respectively, while bond lengths and bond angles are kept fixed.

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The SPC/E force field, likewise to TIP4P/2005, is considered one of the best, two-body, non-

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polarizable, water models [61] and has also proved to be accurate in capturing the vapor-liquid

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IFT [59]. SPC/E does not use the experimental geometry of the water but instead two simple

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values for the bond length (1 Å) and angle (109.47˚). The TIP3P is the most commonly used

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water model in biomolecular simulations [61] and it was primarily developed to reproduce its

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density and the vaporization enthalpy at ambient temperature and pressure conditions [56, 61].

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However, several studies have highlighted the TIP3P’s poor performance in describing important

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water properties, thereby expressing serious concerns about its more generalized use [58, 61].

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Despite its known deficiencies, given that the Lipid14 and GAFF force fields have been

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parameterized for use primarily with the TIP3P water model [43] and that this combination is

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utilized in aqueous membrane bilayer simulations [36], this water model was also included in

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this study. The force field parameters of all the species involved are collected and presented in

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Tables S4 and S5 of the Supporting Information document.

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Standard Lorentz–Berthelot combining rules [62] were used for the well depth ε and the

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size parameter σ to describe non-bonded LJ interactions between sites of different type i and j

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according to the expressions:

ε ij = ε iiε jj and σ ij =

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σ ii + σ jj 2

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The Berthelot (geometric mean) combining rule has been shown to work well for

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various properties of several binary mixtures of components, having atoms of similar sizes and

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ionization potentials [63-69]. However, it has been proven to be insufficient in the description of

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dispersion interactions between polar and non-polar components [63]. Previous simulation

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studies have shown that the combination of TraPPE n-alkanes and SPC/E water mixtures yields

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water solubilities that are underestimated by approximately an order of magnitude compared to

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their experimental values [70]. The source of this behavior may be primarily attributed to the

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inaccurate force field description of electrostatic and induction effects of water in n-alkane [71,

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72], as well as the crudely modeled water – n-alkane interactions based on the Lorentz –

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Berthelot combining rules. In order to attain better agreement with experiment, it has become

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customary to introduce corrections in terms of the deviation from the Berthelot rule [70],

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expressed as:

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ε ij = kij ε iiε jj

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where, kij is a binary interaction parameter fitted to the experimental data. Such a parameter was

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also used in the present study, as it was previously found that the interfacial properties of the

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water/n-decane mixture were not sensitive to size parameter σ and the standard Lorentz

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combining rule was employed for the description of unlike sites [26]. 2.2. Simulation details

The initial conformations of all systems were constructed by means of the Amorphous and

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Interface Builder modules integrated in Scienomics MAPS software package [73], according to

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which the constituent molecules were first inserted into the cubic boxes using a modified

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configuration bias scheme [74], which were later merged to produce final orthorhombic cells of

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the interfaces phases. The number of molecules used was 2000 for water and 250 for toluene and

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n-dodecane, respectively. In the ternary water/toluene/n-dodecane mixture, 162 toluene and 88 n-

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dodecane molecules were used, respectively, in order to properly account for the 50:50 (wt/wt)

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toluene/n-dodecane blend requirement of the challenge. Then, the generated GAFF, Lipid14 and

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TIP4P/2005, TIP3P and SPC/E topologies and coordinate files were converted to the

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GROMACS format by means of the ACPYPE utility [75] (Table S5). All topology and

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coordinate files are available as a Mendeley dataset [76].

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The liquid-liquid IFT was obtained by interfacial MD simulations using GROMACS

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5.0.7 software [77-81]. The simulations were performed in orthorhombic boxes, with periodic

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boundary conditions imposed in all directions (Figure 1). Prior to production runs and in order to eliminate any close contacts between atoms, all

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systems were subjected to steepest descent energy minimization for 20,000 steps. Then, short

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equilibration simulations in the canonical (NVT) and isobaric-isothermal-isointerface area

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(NPNAT) ensembles were performed, where PN is the input normal pressure and A the interfacial

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area. Specifically, all systems were gradually heated to the target temperatures for 100 ps in the

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NVT ensemble using the Berendsen thermostat [82], with the coupling constant set to 1 ps. LJ

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interactions were cut-off at 14 Å and the Particle Mesh Ewald (PME) method [83, 84] was

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applied for the calculation of long-range electrostatic interactions at the same cut-off distance.

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The LINCS algorithm [85] restrained all bonds involving hydrogen atoms. The integration step

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of all simulations was set to 2 fs.

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All systems were then equilibrated for a period of 5 ns in the NPNAT ensemble, at

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constant pressure of 1.83 MPa using a Berendsen barostat [82] with the coupling constant set to

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1 ps. Pressure coupling was isotropic in the x and y direction, but semi-isotropic in the z

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direction, which is perpendicular to the liquid-liquid interface. During this period, the density of

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both liquid phases converged to a mean value, along with the energy of the system (Figure 1).

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The IFT, γ , was evaluated by using the diagonal stress tensor elements ( Pxx , Pyy , and

Pzz ) through the following expression [86-88]:

γ=

Pxx + Pyy   1 Lz  Pzz −  2 2  

(3)

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where, Lz is the length of the simulation box in the z direction, normal to the water/oil interface

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which forms along the xy plane. The factor ½ is due to the presence of two interfaces and angle

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brackets represent the ensemble average.

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For the purposes of the challenge, IFTs were calculated without employing any

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modifications to LJ combining rules from a single 5 ns run per state point, in the NPNAT

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ensemble using the Nosé–Hoover thermostat [89], while maintaining the semi-isotropic pressure

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coupling with a Berendsen barostat [82]. IFT values and statistical uncertainties (95% confidence

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intervals) were obtained by dividing the production period of the simulations into five blocks

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(Table S6 of Supporting Information). After the submission to the challenge, longer production

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runs of 10 ns were performed. Each run was executed on 100 Intel Xeon E5-2680v2 cores and

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required approximately two wall-clock hours for completion. The simulation length was found to

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have no impact on IFT results (Table S7 of Supporting Information). It is important to note here,

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that the kij binary interaction parameter was fitted after the end of the challenge and upon

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disclosure of the experimental data.

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The cut-off of the LJ interactions has a minor impact on the molecular arrangement, but

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significantly influences the computed values of properties such as the IFT. This is more profound

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in simulations of inhomogeneous systems, leading to incorrect estimation of interfacial

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properties [59]. Therefore, instead of using analytical tail corrections, we applied the Particle-

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mesh Ewald summation for the attractive LJ interactions (LJ-PME) [90]. This technique is

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computationally robust and has been successfully employed in the calculation of properties such

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as IFT [91]. However, previous works have shown that using LJ-PME with the GAFF force

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field, which has been optimized for a cut-off approach, leads to overestimated IFT for several

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organic liquids [92]. We investigated the effect of using the LJ-PME over the cut-off to the long-

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range LJ potential, using a radius of 16 Å a practice that has shown to be equally efficient [90].

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Our IFT results showed no dependence on the long-range LJ treatment chosen (Tables S7 of

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Supporting Information). Snapshots of the equilibrated structures of all systems are illustrated in

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Figure 1.

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3. Results and Discussion

In this section, the MD simulations results for the series of water/oil mixtures investigated are

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presented. All IFT calculations are at the reference temperatures of 383.15, 403.15, 423.15 and

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443.15 K and pressure of 1.83 MPa. 3.1.

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Berthelot combining rule

The density profiles illustrated in Figure 1, show that the bulk region densities of water

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(TIP4P/2005) and n-dodecane (Lipid14) are close to their experimental values [93]. Toluene

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density is slightly underestimated by GAFF compared to its experimental value, a finding also

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reported by Caleman et al. at 298.15 K and 1 bar [45]. Furthermore, the density distribution of

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the water/toluene/n-dodecane mixture components is in agreement with previous simulation

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studies of water/oil interfaces, particularly with regard to the tendency of the toluene molecules

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to accumulate at the water interface (Figure 1c) [28]. This accumulation phenomenon at water/oil

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interfaces is attributed to the weak hydrogen bonding between water and toluene at the interface

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[49]. These density distribution profiles are essentially the same for SPC/E, with the partial

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density being slightly underestimated compared to the experimental values at each temperature

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(Figure S3 of Supporting Information). On the other hand, in the TIP3P water systems the

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underestimation of water density becomes more significant, a feature which should have an

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important effect on the accurate calculation of IFTs (Figure S4).

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From the results presented in Table 1, it is indicated that the IFT values in all systems

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and for all force fields studied decrease as temperature increases, reproducing the experimentally

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observed trends. Figure 2 shows that there is an almost linear dependence between γ and T; this

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behavior is in agreement with previous experimental studies on water – n-alkane mixtures [13].

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The water/n-dodecane mixture exhibits higher IFT compared to water/toluene, with the

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water/toluene/n-dodecane mixture adopting intermediate values.

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These observations are in line with the experimental values used as a benchmark for the

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purposes of the challenge (Figure 2). However, even though the combination of the GAFF and

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Lipid14 AMBER force fields with TIP4P/2005 appears to capture the correct trend, absolute IFT

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values are overestimated compared to the experimental ones by 20%, 27% and 30% on average

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for the water/toluene, water/n-dodecane and water/toluene/n-dodecane mixtures, respectively.

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The SPC/E displays the same behavior with TIP4P/2005. Furthermore, the overestimation is

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increasing with increasing temperature. It is also clear that the TIP3P water model has a

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profound impact on IFT. Specifically, the IFT results of all mixtures are now underestimated but

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are slightly closer in absolute value compared to the experimental benchmark data. Furthermore,

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the TIP3P model leads to an improvement in the description of the IFT temperature dependence,

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especially in the case of the water/toluene mixture.

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It is useful to note here that all water models have similar σ values for water oxygen,

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with differences in their ε values (Table S4 of the Supporting Information). In fact, the ε values

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decrease in the order εTIP4P/2005>εSPC/E>εTIP3P. Thus, by altering the εij of the toluene and n-

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dodecane carbon and water oxygen atoms, respectively, one can fine-tune these models in order

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to achieve better agreement with the experimental IFT values.

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3.2.

Modified Berthelot combining rule

The simulations with scaled binary interaction parameters of the toluene and n-dodecane carbon

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and water oxygen atoms, respectively, resulted in better agreement with experiment. The kij

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values led to the most accurate results are presented in Table 2. One can observe that the

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TIP4P/2005 and SPC/E models were found to perform better with different kij for the aromatic

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and alkyl carbons with water oxygen. On the other hand, mixtures with the TIP3P model were in

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better agreement by setting a uniform kij = 0.8 value for all carbon atoms with water oxygen

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interactions. From the results listed in Table 3 and depicted in Figure 3 become clear that the

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fine-tuning of the kij parameter can produce much improved water/oil IFT values. Nevertheless,

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upon closer examination, one can isolate subtle differences introduced to the simulations by the

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choice of water model.

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The average absolute difference of simulated and experimental IFT values is ~2% for

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the water/toluene and water/n-dodecane mixtures for all water models used. This translates to an

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absolute difference of 1 mN/m. Despite the overall improvement, there seems to be a

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discrepancy that is not tackled even after the introduction of the kij parameter. More specifically,

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it is observed that the simulations including TIP4P/2005 and SPC/E systems show better

17

agreement with experiments at lower temperatures, which is not followed at higher temperatures.

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This results in a different temperature dependence of IFT, which diverges from the experimental

19

trend. The TIP3P model coupled with GAFF and Lipid14 for toluene and n-dodecane,

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respectively, results in better reproduction of the data for the entire temperature range examined.

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This can be attributed to the compatibility of the TIP3P model with the AMBER family of force

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fields.

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Deviation from experiment becomes more pronounced in the case of the

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water/toluene/n-dodecane mixture. Calculated IFT values deviate by about 8%, which translates

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to approximately 3 mN/m on average for all systems. Similarly to the findings for the binary

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mixtures, the TIP4P/2005 / GAFF / Lipid14 and SPC/E /GAFF / Lipid14 combinations result to

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IFTs that are closer to the experimental values at lower temperatures, while adopting slightly

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higher values compared to experiment as temperature increases (Table 3 and Figure 3). The

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TIP3P / GAFF / Lipid14 combination shows the most consistent behavior, but IFT values are

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still overestimated by approximately 6%. This indicates that even though the simple kij scaling

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approach is adequate for improving results for the binary water/oil mixtures, it is not enough to

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capture the more complex intermolecular interactions in ternary water/oil/oil mixtures. There appear to be significant differences in the interfacial loading of toluene depending

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on the water model used, which explains the differences in IFT. Given the different electrostatics

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of each water model, the attractive “weak hydrogen bonding” between the aromatic toluene and

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water molecules [28] is either enhanced (TIP4P/2005, SPC/E) or reduced (TIP3P). This explains

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the difference in toluene density observed with either water model (Figure 4a). The preference of

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toluene to accumulate near the water interface in the water/toluene/n-dodecane mixture, not only

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explains the intermediate IFT values of the ternary compared to the binary mixtures, but also

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renders toluene loading at the interface as a controlling factor of the IFT.

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From our simulations, it becomes clear that the use of the kij adjustable parameter alone

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is insufficient to predict accurately the experimental IFT data for ternary water/oil/oil mixtures.

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Fine-tuning the kij parameter results into a toluene density profile at the water/oil interface that

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is now common for all systems (Figure 4b). This highlights the role of toluene as an active

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interfacial agent in the ternary mixture. 14

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4. Conclusions The present work entails extensive MD simulations of representative water/oil binary and ternary

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mixtures for the calculation of IFT. Our efforts concentrated primarily in incorporating atomistic

4

force fields that have been primarily developed for biomolecular simulations in addressing

5

industrially related properties like the IFT. The GAFF and Lipid14 force fields were employed

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for the description of toluene and n-dodecane, respectively. The partial density profiles of the oil

7

phases were found to be in agreement with the respective experimental data. These molecular

8

models were combined with three fixed-point-charge water models, namely the TIP4P/2005,

9

TIP3P and SPC/E. The TIP3P model does not reproduce the experimental water density as

10

accurately as its TIP4P/2005 and SPC/E counterparts do. Water model parameters are crucial in

11

the prediction of IFT properties, as they are responsible for the significant overestimation

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(TIP4P/2005 and SPC/E) or the moderate underestimation (TIP3P) of IFT values compared to

13

the experimental data.

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Modifying the cross LJ interactions by appropriately adjusting the binary interaction

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parameter is a simple but effective way to improve the accuracy of the IFT predictions for binary

16

mixtures. However, even by following this approach, the use of the TIP4P/2005 and SPC/E

17

models leads to slightly overestimated IFT values at 443.15 K, weakly diverging from the

18

experimental weak temperature IFT dependence. Surprisingly, the combination of the less

19

accurate TIP3P water model with the aforementioned AMBER force fields, using a uniform

20

kij = 0.8 parameter of the scaling of carbon-water oxygen interactions captures the overall IFT

21

behavior more accurately compared to the other two water models. TIP3P’s deficiency in

22

accurately reproducing water density at the conditions examined is compensated by its

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compatibility with the AMBER force fields and aids towards calculation of IFTs that are in

2

better agreement with experiment. As far as the water/toluene/n-dodecane mixture is concerned, all simulations, regardless

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of the kij scaling used, led to overestimated IFT values compared to experimental findings. The

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TIP4P/2005 and SPC/E model behavior in higher temperatures pertains, while the TIP3P model

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shows better agreement. The overestimation of IFT for the ternary mixture cannot be

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compensated by the introduction of a simple kij binary parameter. The source of this discrepancy

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can be attributed to the initial atomistic force field parametrization of the pure components and to

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the actual combining rules used. Therefore, improved models that include IFT data into their

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initial setup may lead to more accurate mixture calculations.

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AUTHOR INFORMATION Corresponding Authors

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*IGE: [email protected]

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Author Contributions

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The manuscript was written through contributions of all authors. All authors have given approval

17

to the final version of the manuscript.

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Acknowledgments

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This work was supported by computational time granted from the Greek Research & Technology

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Network (GRNET) in the National High Performance Computing facility - ARIS - under project

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ID002043. We are also thankful to the High Performance Computing center of Texas A&M

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University at Qatar for generous resource allocation. Scienomics SARL is acknowledged for

24

providing MAPS software used to generate initial structures of the systems simulated.

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Table 1. Calculated IFT values for the various mixtures with the three different water models

2

examined, without any scaling of the intermolecular interaction parameters ( kij =1).

γ (mN/m) water/toluene

20.8 ± 0.6

443.15

25.9 ± 0.7

18.8 ± 0.6

SPC/E

29.0 ± 0.6

29.4 ± 0.8

15.3 ± 0.6

27.1 ± 0.7

Experiment

31.2 ± 1.0

31.1 ± 0.5

SC

22.8 ± 0.3

M AN U

423.15

33.1 ± 0.7

TIP3P

403.15

TIP4P/2005

383.15

RI PT

T (K)

28.6 26.4 23.8

24.8 ± 0.9

20.2

36.8 ± 1.2

45.3 ± 1.2

40.0

33.4 ± 0.7

42.6 ± 0.7

443.15

32.9 28.5

31.4

water/toluene/n-dodecane 28.9 ± 0.6

37.5 ± 0.3

36.4 ± 0.3

26.6 ± 1.1

35.3 ± 0.3

31.6 ± 0.9

36.5

36.1 ± 0.9

38.7 ± 0.8

34.7 ± 0.4

Experiment

SPC/E

26.1 ± 0.4

39.9 ± 1.0

23.6 ± 0.6 20.6 ± 0.4

32.9 ± 0.5 29.0 ± 0.6

Experiment

423.15

29.5 ± 0.6

SPC/E

403.15

TIP4P/2005

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383.15

38.5 ± 1.1

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443.15

42.4 ± 0.8

TIP3P

423.15

45.4 ± 0.8

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403.15

47.5 ± 0.8

TIP4P/2005

383.15

TIP3P

water/n-dodecane

29.0 26.1 22.6

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Table 2. Binary interaction parameter values used for IFT predictions. The atom types refer to

2

the interaction sites of toluene (ca: aromatic, c3: aliphatic) and n-dodecane (cD: aliphatic)

3

carbons with water oxygen (OWT4: TIP4P/2005, OW: TIP3P and SPC/E oxygen types; for the

4

actual force field parameters see Tables S1 and S4 of the Supporting Information).

Water model

SPC/E

Value Pair type Value Pair type Value

5

OWT4-ca

OWT4-cD

1.25

1.05

1.25

OW-c3 0.80 OW-c3

OW-ca

OW-cD

0.80

0.80

OW-ca

OW-cD

1.20

1.05

1.20

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OWT4-c3

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TIP3P

Pair type

n-dodecane

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Table 3. Calculated IFT values with 95% confidence intervals using the three different water

2

models, using parameters shown in Table 2.

γ (mN/m) water/toluene

24.6 ± 0.6

443.15

22.7 ± 0.8

26.5 ± 0.4

23.6 ± 0.4

20.2 ± 0.5

24.6 ± 0.7

Experiment

27.2 ± 0.4

SPC/E

26.2 ± 0.3

28.4 ± 0.2

SC

29.6 ± 0.9

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423.15

28.1 ± 0.9

TIP3P

403.15

TIP4P/2005

383.15

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T (K)

28.6 26.4 23.8

22.1 ± 0.4

20.2

39.8 ± 1.0

40.0 ± 1.3

40.0

36.2 ± 0.5

36.2 ± 0.7

443.15

31.4 ± 1.1

33.6 ± 0.5

33.2 ± 0.8

30.5 ± 0.8

31.3 ± 0.6

30.8 ± 0.7

27.2 ± 0.8

36.5 32.9 28.5

water/toluene/n-dodecane

32.6 ± 0.6

29.0 ± 0.9

Experiment

SPC/E

28.4 ± 0.4

33.6 ± 0.9

27.4 ± 0.7 23.9 ± 0.6

28.3 ± 0.5 25.9 ± 0.5

31.4

Experiment

423.15

32.7 ± 0.3

SPC/E

403.15

TIP4P/2005

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383.15

31.0 ± 0.8

EP

443.15

33.7 ± 0.9

TIP3P

423.15

36.7 ± 0.8

TE D

403.15

38.7 ± 1.2

TIP4P/2005

383.15

TIP3P

water/n-dodecane

29.0 26.1 22.6

3 4

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Figure 1. Equilibrated structures and partial densities of all systems studied using the

3

TIP4P/2005 water model, for various temperatures and pressure 1.83 MPa. Water, toluene and n-

4

dodecane molecules are illustrated in red, gray and cyan colors, respectively.

5

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Figure 2. Calculated IFT of water/toluene, water/n-dodecane and 50:50 (wt/wt) water/toluene/n-

3

dodecane mixtures with the TIP5P/2005, TIP3P and SPC/E water models, without scaling of the

4

intermolecular interaction parameters.

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Figure 3. Calculated IFT of water/toluene, water/n-dodecane and 50:50 (wt/wt) water/toluene/n-

3

dodecane mixtures with the TIP5P/2005, TIP3P and SPC/E water models, by scaling the

4

intermolecular carbon – oxygen interaction parameters. Binary interaction parameter values used

5

for IFT predictions depending on the water model are provided in Table 2.

6

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Figure 4. Density profiles for the components of the ternary water/toluene/n-dodecane mixture at

3

383.15 K a) without and b) with scaling of the intermolecular carbon – oxygen interaction

4

parameters (Table 2) for all force fields used.

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